On the Distance Sets of Self-Similar Sets
Dynamical Systems
2012-05-30 v2
Abstract
We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one.
Keywords
Cite
@article{arxiv.1110.1934,
title = {On the Distance Sets of Self-Similar Sets},
author = {Tuomas Orponen},
journal= {arXiv preprint arXiv:1110.1934},
year = {2012}
}
Comments
13 pages, one figure; exposition clarified and typos corrected in v2; to appear in Nonlinearity